1. Equations & Inequalities

What is an identity equation? Give an example.

Solve and check each linear equation. 3(x - 1) = 21

Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 3-5(2x + 1) - 2(x-4) = 0

Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. (3x+1)/3 - 13/2 = (1-x)/4

Solve each equation. 2x/(x-2) = 5 + 4x²/(x-2)

In Exercises 1–26, solve and check each linear equation. 3(x - 8) = x

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 5/2x - 8/9 = 1/18 - 1/3x

Resistance of a Wire The resistance in ohms of a platinum wire temperature sensor varies directly as the temperature in kelvins (K). If the resistance is 646 ohms at a temperature of 190 K, find the resistance at a temperature of 250 K.

Solve each equation. | (6x + 1)/ (x - 1) | = 3

Solve each problem. If y varies inversely as x, and y=10 when x=3, find y when x=20.

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - (x - 3)/2 = (x + 2)/3

Determine the values of the variable that cannot possibly be solutions of each equation. Do not solve.

(5/(2x+3))-(1/(x-6))=0

Solve each problem. The speed of a pulley varies inversely as its diameter. One kind of pulley, with diameter 3 in., turns at 150 revolutions per minute. Find the speed of a similar pulley with diameter 5 in.

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4/(x - 2) + 3/(x + 5) = 7/(x + 5)(x - 2)

Determine the values of the variable that cannot possibly be solutions of each equation. Do not solve. 1/(4x) - 2/x = 3